Comically wrong — what can happen when you ignore physics

Superman flies through the sky, and throws a heavy asteroid at the speed of a bullet. He is shown in the next panel stationary and triumphant. Except, you know, this violates physics.

When writing, the simplest things can come back to bite you. As it turns out, Superman is actually flying backward with a recoil velocity of around 800,000 meters per second (m/s), or around 2 million miles per hour, which creates a few problems if there are spaceships in the way of Superman, or if you need Superman to save the world again.

This sort of thing is why knowing a little classical physics can come in handy (if your story takes place at an atomic scale or inside a black hole, I don’t know what to tell you except that this stuff doesn’t apply there). First, let’s start by establishing some more specific parameters for the problem.

The average asteroid weighs around 100,000 kg (rounded down for ease), and the average American male weighs around 100 kg (rounded up for ease), so the asteroid is around 1000 times more massive than Superman (this is all approximate, obviously).

The speed of a bullet is around 800 m/s. Now for the actual physics. The law of conservation of momentum says that the momentum going into and coming out of a situation must be equal. Momentum is equal to mass times velocity. Now, before Superman was throwing any asteroids, he was stationary, and so he had no momentum (0 times anything is 0). Ditto for the asteroid — we’ll assume it wasn’t going anywhere either.

So the momentum before and after Superman throwing the asteroid is 0 (units here, for you nerds, are kg m/s). We know the momentum after the throw is equal to the asteroid’s momentum plus superman’s momentum. Now that we have these parameters established, we can go about calculating Superman’s recoil velocity.

Momentum = mass times velocity. The asteroid’s mass is 1000x (we’ll ignore Superman’s exact weight; we don’t need it) and its velocity is 800 m/s, giving the asteroid a momentum of 800,000x kg m/s — and remember, Superman’s momentum must be the opposite! The negative sign here really means Superman is flying away from the asteroid, so we’ll just ignore it and calculate his speed, knowing that his direction is away from the asteroid.

So, we can set up the equation 800,000x kg m/s = x kg (remember, this is Superman’s weight) times his recoil speed. We divide both sides by his weight, leaving us with 800,000 m/s for his recoil speed (and remember, he is going away from the asteroid, so that’s his recoil velocity)! This is quite different from a standstill.

Let’s look at some interesting consequences of this recoil velocity. First, let’s say there’s another emergency that Superman needs to take care of (or Clark Kent needs to get back to work). In a minute, Superman will be 48,000,000 meters, or 48,000 kilometers, away from Earth. In an hour, Superman will be 192,000 kilometers away. To put these numbers in perspective, the Moon is around 384,000 kilometers away — in other words, by the time an hour has passed, Superman will be halfway to the moon.

What sort of force could stop Superman? First, let’s calculate his kinetic energy, which is 1/2 times mass times velocity squared. Superman, we said, is around 100 kg, and his velocity is 800,000 m/s, producing a kinetic energy of 3.2 times 10 to the 13th joules. From there, let’s use the equation Energy = force times distance, or to rearrange, force = energy divided by distance. Let’s say we want to stop Superman over a distance of a kilometer — we’d have to apply a force of 3.2 times 10 to the 13th newtons to stop him.

To put this into perspective, the space shuttle has 28 million newtons of thrust. If Superman had (for whatever reason) a rocket ready to start blasting, it would need to be 5,120,000 times more powerful than the space shuttle. The Saturn V rocket, the most powerful rocket ever made, had 35,100,000 newtons of thrust — here, the rocket strapped to Superman’s back would need to be 911,681 times more powerful.

Now, according to Newton’s third law, every action has an equal and opposite reaction. This means that not only is Superman stopping (finally, over a whole kilometer), but there’s a force of 3.2 times 10 to the 13th newtons being applied to him! What force can a human handle before getting killed (ignoring Superman’s super-ness for the moment)?

Force = mass times acceleration; we know Superman’s mass and the force being applied to him, so his acceleration must be 320,000,000,000 m/s squared. If we convert this to g-force (I’m rounding g to 10 here instead of 9.8), we have a force of 32,000,000,000g. This is insane. According to Wikipedia, the maximum g-force anyone has lived through was 214g, and that very briefly, and they received many injuries. Superman’s experiencing this g-force over an entire kilometer.

So, in the end, we have a dead, out-by-the-moon Superman, and an asteroid hurtling off somewhere. Too bad Superman didn’t study physics in highschool…

For the curious

While the first problem posed in this article (Superman’s recoil velocity) is a not uncommon physics textbook problem (see for example Conceptual Physics, by Paul Hewitt, page 109, problem 9), it is probably based off of a real comic.